Compute

$\frac{1622^2-1615^2}{1629^2-1608^2}$.
Solution: The numerator factors as $(1622-1615)(1622+1615)=7(3237)$.

The denominator factors as $(1629-1608)(1629+1608)=21(3237)$.

Thus the fraction is equal to

$$\frac{7(3237)}{21(3237)}=\frac{7}{21}=\boxed{\frac{1}{3}}$$